Hybrid Formulation of Three-dimensional Limit Analysis

Abstract

The authors have proposed a hybrid type formulation of rigid plastic finite element method for two-dimensional problems. This formulation has been modified to handle with shear locking and hourglass mode with the introduction of the linearly distributed stresses within an element. In the context of previous studies, a hybrid type rigid plastic finite element method for three-dimensional problems is investigated in this paper. Firstly, spacial discretization of a stress field in an element is discussed. Secondly, a numerical code is developed with the implementation of the abovementioned stress distribution. Finally, four example problems, i.e., plastic load of a plate with a hole, stability of a tube with defects under inner pressures or bending moments, stability of conical slopes and bearing capacity of circular footing are solved to check the numerical performance of the developed code. The results show good agreements with others' studies. It can be concluded that the numerical method proposed in this paper is reliable and promising.